RECORD
Constituent Quark Model versus Nonperturbative QCD
High Energy Physics - Phenomenology · Submitted 5 May 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Such a mechanism, if it is correct, would be an explanation of the phenomenological success of the dimensional counting rules at available, very modest energies for many different processes.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We discuss a few, apparently different (but actually, tightly related) problems: 1. The relation between QCD and valence quark model, 2. The asymptotic behavior of the nonperturbative pion wave function $\psi(\k, x)$ at $x\rightarrow 0,~1, \k \rightarrow \infty$ and 3. The dimensional counting rules in the intermediate region of energy. The analysis is based on such general methods as dispersion relations, duality and PCAC. We calculate the asymptotic behavior of the wave function ($wf$) at the end-point region ($x\rightarrow 1$ and $\k\rightarrow\infty$) by analysing the corresponding large $n-$th moments in transverse $\la\vec{k}_{\perp}^{2n}\ra \sim n!$ and longitudinal $\la (2x-1)^n\ra \sim 1/n^2$ directions. This information fixes the asymptotic behavior of $wf$ at large $\k$ ( which is turned out to be Gaussian commonly used in the phenomenological analyses). We discuss some applications of the obtained results. In particular, we calculate the nonleading ``soft" contribution to the pion form factor at intermediate momentum transfer. We argue, that due to the specific properties of $\psi(\k, x)$, the corresponding contribution can temporarily {\bf simulate} the leading twist behavior in the extent region of $ Q^2 $. The same effect also takes place for the nucleon formfactor. Such a mechanism, if it is correct, would be an explanation of the phenomenological success of the dimensional counting rules at available, very modest energies for many different processes. We discuss some inclusive amplitudes also.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss a few, apparently different (but actually, tightly related) problems: 1. | contribution 0.52 | 0.60 | 0.02 | unclear 0.80 |
| s1 | The relation between QCD and valence quark model, 2. | background 0.64 | 0.14 | 0.02 | unclear 0.96 |
| s2 | The asymptotic behavior of the nonperturbative pion wave function $\psi(\k, x)$ at $x\rightarrow 0,~1, \k \rightarrow \infty$ and 3. | background 0.70 | 0.16 | 0.03 | unclear 0.89 |
| s3 | The dimensional counting rules in the intermediate region of energy. | background 0.62 | 0.23 | 0.03 | unclear 0.86 |
| s4 | The analysis is based on such general methods as dispersion relations, duality and PCAC. | method 1.00 | 0.38 | 0.02 | asserted 0.99 |
| s5 | We calculate the asymptotic behavior of the wave function ($wf$) at the end-point region ($x\rightarrow 1$ and $\k\rightarrow\infty$) by analysing the corresponding large $n-$th moments in transverse $\la\vec{k}_{\perp}^{2n}\ra \sim n!$ and longitudinal $\la (2x-1)^n\ra \sim 1/n^2$ directions. | method 0.83 | 0.94 | 0.12 | asserted 1.00 |
| s6 | This information fixes the asymptotic behavior of $wf$ at large $\k$ ( which is turned out to be Gaussian commonly used in the phenomenological analyses). | result 0.94 | 0.88 | 0.19 | asserted 0.99 |
| s7 | We discuss some applications of the obtained results. | contribution 0.94 | 0.67 | 0.03 | asserted 0.52 |
| s8 | In particular, we calculate the nonleading ``soft" contribution to the pion form factor at intermediate momentum transfer. | contribution 0.77 | 0.95 | 0.07 | asserted 1.00 |
| s9 | We argue, that due to the specific properties of $\psi(\k, x)$, the corresponding contribution can temporarily {\bf simulate} the leading twist behavior in the extent region of $ Q^2 $. | interpretation 0.97 | 0.73 | 0.34 | hedged possibility 0.58 |
| s10 | The same effect also takes place for the nucleon formfactor. | result 0.91 | 0.58 | 0.06 | asserted 1.00 |
| s11 | Such a mechanism, if it is correct, would be an explanation of the phenomenological success of the dimensional counting rules at available, very modest energies for many different processes. | interpretation 1.00 | 0.26 | 0.51 | hedged possibility 0.81 |
| s12 | We discuss some inclusive amplitudes also. | contribution 0.99 | 0.73 | 0.03 | asserted 0.68 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We discuss a few, apparently different (but actually, tightly related) problems: 1. The relation between QCD and valence quark model, 2. The asymptotic behavior of the nonperturbative pion wave function $\psi(\k, x)$ at $x\rightarrow 0,~1, \k \rightarrow \infty$ and 3. The dimensional counting rules in the intermediate region of energy. The analysis is based on such general methods as dispersion relations, duality and PCAC. We calculate the asymptotic behavior of the wave function ($wf$) at the end-point region ($x\rightarrow 1$ and $\k\rightarrow\infty$) by analysing the corresponding large $n-$th moments in transverse $\la\vec{k}_{\perp}^{2n}\ra \sim n!$ and longitudinal $\la (2x-1)^n\ra \sim 1/n^2$ directions. This information fixes the asymptotic behavior of $wf$ at large $\k$ ( which is turned out to be Gaussian commonly used in the phenomenological analyses). We discuss some applications of the obtained results. In particular, we calculate the nonleading ``soft" contribution to the pion form factor at intermediate momentum transfer. We argue, that due to the specific properties of $\psi(\k, x)$, the corresponding contribution can temporarily {\bf simulate} the leading twist behavior in the extent region of $ Q^2 $. The same effect also takes place for the nucleon formfactor. Such a mechanism, if it is correct, would be an explanation of the phenomenological success of the dimensional counting rules at available, very modest energies for many different processes. We discuss some inclusive amplitudes also.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.